Case study analyses of A12139 and Al2198 laser welds are presented. These analyses demonstrate the concept of constructing parameter spaces for prediction of properties within the heat-affected zone (HAZ) of welds using inverse modeling, which are in turn for process control. The construction of these parameter spaces consists of two procedures. One procedure entails calculation of a parameterized set of temperature histories by inverse analysis of the heat deposition occurring during welding. The other procedure entails correlating these temperature histories with a specific physical property of the weld that is measurable. The analyses presented here examines some characteristics of inverse modeling with respect to the prediction of hardness within the HAZ for deep penetration laser welding of the Aluminum alloys A12139 and Al2198. This study further demonstrates the feasibility of constructing a parameter space for the prediction of weld properties using weld cross section measurements that are independent of weld process conditions.